Slowdown with @fastmath and complex numbers

[KristofferC]

using BenchmarkTools 

function fractal(z, c, lod)
   for i in 1 : lod
          @fastmath (abs(z) > 2) ? (return i) : (z = z^2 + c) 
   end
   return lod
end

julia> @btime fractal(1im,1im,1)
  46.854 ns (2 allocations: 48 bytes)

Removing @fastmath:

julia> @btime fractal(1im,1im,1)
  9.455 ns (0 allocations: 0 bytes)

Ref: #19298

One problem is the type instability where z first is a Complex{Int64} and then turned into a Comlex{Float64} after the exponentiation. Fixing this removes the allocation but doesn't change the execution speed:

julia> @btime fractal(1.0im, 1.0im, 1)
  46.405 ns (0 allocations: 0 bytes)

Edit: It seems that the fast macro makes the exponent dispatch to a function that promotes both numbers to complex.

Edit2: Fixing the above, it turns out that the generic power by squaring is faster anyway up to an exponent of ~ 1000000000...

Edit3: The @fastmath macro also destroys the Val{2} exponent optimization in the lowering since the syntax is rewritten to pow_fast(z, 2).

[ajkeller34]

re: edit3: #21099 has been open for a while. It'd be nice to either merge or close that.

[KristofferC]

Runs at same speed now.